Characteristics Of 1D Photonic Crystal Sensor With Two Defects

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Characteristics Of 1D Photonic Crystal Sensor With Two Defects

Mardanih

^{1, 3, #}

, T. P. Negara

²

, H. Hardhienata

³

, H. Alatas

³

1)Graduate School of Biophysics, Bogor Agricultural University, Bogor 16680, Indonesia

2)Computer Science Department, Pakuan University, Jl. Pakuan, Bogor 16143, Indonesia

3)Theoretical Physics Division, Department of Physics, Bogor Agricultural University Jl. Meranti, Kampus IPB Darmaga, Bogor 16680, Jawa Barat, Indonesia

#)Corresponding author. E-mail: [email protected]

Abstract. Numerical simulations of electromagnetic wave propagation inside a one-dimensional (1D) photonic crystal with two defect rods are presented. The simulations were carried out by applying Finite Difference Time Domain (FDTD) method to solve the corresponding Maxwell equations. The result shows a linear dependence of time average energy density with respect to the variation of second defect refractive index, which can be potentially used for refractive index sensing platform. On the other hand, a non-linear dependence of time average energy density is obtained by varying the radius of the second defect.

Keywords: Photonic Crystal, FDTD, PML, Optical Sensor PACS: 42.82.Et, 41.20.Jb, 42.70.Qs

INTRODUCTION

The unique characteristics of an electromagnetic wave when interacting with photonic crystals can be applied to build an optical sensor that interacts with certain material which if designed accordingly can meet specific needs [1]. The optical sensor model described in this paper consists of a one-dimensional (1D) photonic crystal (PhC) imbedded by two defects.

Numerical simulations were performed by applying the Finite Difference Time Domain (FDTD) method [2].

A sensor will work if there is a strong interaction between the sensor and sample material. However previous research on a 1D PhC optical sensor for index measurement is that it will only work for a specific sample material within a certain measurable range [3].

Currently sensors with more optimal abilities and higher measurable lengths as well as higher sensitivity are of high demand. One of the alternatives to meet this objective is to build a sensor based on PhC. This sensor applies the principles of electromagnetic wave propagation inside optical mediums with certain refractive index.

In this paper we describe results from our numerical studies on a 1D PhC with a model that

consists of 11 dielectric rods arranged horizontally in the x−axis inside a material with the addition of two defect rods namely at the fourth and eighth positions by referring to the 1D PhC studied previously [3]. The model of the structure is depicted in Fig. 1. The incident wave is propagating from the right side of the material along the x−axis.

PHYSICAL MODEL AND MATHEMATICAL FORMULATION

The Maxwell equation with no current sources for transverse magnetic (TM) modes where the magnetic field, H lies in the x−y plane and the electric field, E is parallel to the z axis can be written as [2]:













∂

−∂

∂

= ∂

∂

y H x H t

D_z _y _x

0 0

1 µ

ε , (1)

y E t

H_x _z

∂

− ∂

∂ =

∂

0 0

1 µ

ε , (2)

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x E t

H_y _z

∂

= ∂

∂

0 0

1 µ

ε . (3)

Whereas the relation between the z−axis electric field component,E_z and its displacement current D_zin the three equation are [2]

z r

z E

D =ε₀ε (4)

In the simulation we defined our computational boundary by imposing a perfectly matched layer (PML) that has been introduced by Berenger [4].

Inside the PML area, the magnetic and electric conductivity are arranged so that there are no reflection effects in the computational boundary.

As shown in Fig. 1, the model of our optical sensor consists of a silicon (Si) slab with refractive index of 3.48 that was inserted by eleven dielectric rods arranged along x−axis, with rods no. 4 and no. 8 were considered as defects. The slab thickness and length were 2×10³nm and 17.5×10³nm, respectively.

Meanwhile, the corresponding material used for the regular rods was SiO₂

(

n=1.44

)

with radius of 400 nm, whereas Al2O3

(

n=1.7

)

was used for the first defect and the material in the second defect was varied. The radius of the regular rods was 600 nm.

The material variation in the second defect will affect the output energy which is defined as

( )

^t ⁼

∫

^h ^E

( )

^t ^dy

Q

0

r 2

ε (7)

Further, we define the following time average energy density parameter

∫ ( )

=

t

dt t Q t W

0

1 (8)

to characterize the performance of the sensor device.

Here, t denotes the measurement time.

RESULTS AND DISCUSSION

In our simulation we used a mesh number of 200

400× with each mesh having a size of nm

=50

∆

=

∆x y , while the time step is taken to be 8.33 10 ps5

∆ =t × . This simulation was performed by using a plane wave with operational wavelength of 560 nm.

As shown in Fig. 2, inside the structure the field decreases. This is probably due to the operational wavelength whose value is actually located inside the band-gap, as indicated by high amount of back reflected field.

FIGURE 2. (Color) Distribution pattern of the electric field inside the optical sensor after propagating for 260,5 ps. The second defect consists of a dielectric material with a refractive index of 1.40.

FIGURE 3. Change in the time average energy density with respect to variation in the refractive index

of the second defect for a defect radius of 300 nm (solid-square) and a defect radius of 800 nm (solid-

circle) 1^stdefect 2^nddefect

Incident wave

defek

z x y

FIGURE 1. Sketch of 1D Photonic Crystal with two defect rods and homogeneous in z-direction

314

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The other feature that was simulated is the effect of changing the refractive index of the second defect for a fix rod radius and measure the energy density at the output. In this case the energy density is increasing steadily. It is interesting to investigate why the energy density increases.

It is readily seen from Fig. 3 that the effect of different second defect rod radius leads to distinct characteristics of the time average energy density, W.

For a defect radius of 800 nm we found that the simulation results shows a relatively sensitive response as is evident by the steep and linier like increase of W with respect to the second defect refractive index. In the contrary, this is not the case for a defect radius of 300 nm which shows a relatively unchange W value if the refractive index of the second defect is varied.

The 800 nm defect rod feature can thus be utilized to build an optical based index sensor. Good sensors are accurate, sensitive, and have a wide sensing range, thus linearity and stability are the necessary parameter changes. These requirements are met by this sensor.

Further, the effect of changing the second defect rod radius is given in Fig. 4 for the corresponding refractive index of 1.40. It can be inferred that increasing the second defect radius accounts to a non- monotonous decrease in the energy density at the output with the highest value for W obtained for a rod radius of 400 nm and lowest for 800 nm.

This particular feature can be explained by considering that increasing the defect radius will add to the materials ability to affect the electric. An interesting feature can be seen if the radius is increased to 450 nm because it produces a significant energy

density drop before increasing again if the radius is further increased and then keep on decreasing. This pattern repeats itself for a defect radius of 700 nm.

It can be seen from Fig. 4 that the highest energy density is obtained for a defect rod radius of 400 nm and the smallest energy density is found for a defect radius of 800 nm.

CONCLUSION

We have studied the characteristics of 1D PhC with two defects by means of FDTD method. We found that increasing the second defect refractive index with a radius of 800 nm will produce a linier dependence of the time average energy density for n=1.33 to 1.45, which can be potentially applied for an optical based refractive index sensor. A non-linear time average energy density characteristics for a certain refractive index is obtained if the rod of the second defect is increased from 300 nm to 800 nm.

REFERENCES

1. W. C. L. Hopman, P. Pottier, D. Yudistira, J. Van Lith, P. V. Lambeck, R. M. De La Rue, A. Driessen, H. J. W.

M. Hoekstra, and R. M. de Ridder, IEEE J. Select. Top.

Quant. Electron. 11, 11-16 (2005) 2. A. Taflove, S.C. Hagness, Computational

Electrodynamics: Finite-Different Time-Domain Method 2^nd Ed. London: Artech House, 2000.

3. H. Alatas, H. Mayditia, A. A. Iskandar and M. O. Tjia, Jpn. J. Appl. Phys., 45, 6754-6758 (2006).

4. P. Bérenger, Perfectly Matched Layer (PML) for Computational Electromagnetics, Arcueil: Morgan &

Claypool Publisher, 2007.

FIGURE 4. Change in time average energy density with respect to second defect rod radius with refractive

index of 1.40.

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